Children's Minister James Reilly has formally requested that the Government divests itself of all shares in tobacco companies.
Dr Reilly wrote to Finance Minister Michael Noonan last month after being informed that the State has investments worth €10m in tobacco companies through the National Pension Reserve Fund (NPRF).
The Dublin North TD and former Health Minister highlighted the example of Norway, informing Mr Noonan that the Norwegian government had taken such an approach previously.
"I think it would be appropriate if, over a short period of time, we followed Norway's example and the National Pension Reserve Fund divested itself of all shares in tobacco companies," Dr Reilly wrote.
His demand came in the same week that new legislation was passed here that paves the way for the introduction of plain cigarette packaging.
Tobacco companies including Imperial Tobacco and Silk Cut owner Japan Tobacco International have threatened legal action over the plan to force them to sell their products without branded packaging.
Ireland would be the first country in Europe and only the second in the world, after Australia, to force tobacco firms to use plain packaging.
The new packaging would be fully phased in by May 2017.
The NPRF, which is changing to become the Ireland Strategic Investment Fund (ISIF), owns stakes and has interests in tobacco firms including British American Tobacco (BAT) that currently total just under €10m.
At the end of 2013, the NPRF owned nearly 76,000 shares in BAT, which at the time were worth almost €3m at the time.
BAT, whose chairman is former Irish Distillers boss and one-time Bank of Ireland governor Richard Burrows, owns brand such as Rothmans, Pall Mall and Dunhill.
The NPRF had also invested in financial bonds issued by Imperial Tobacco, the owner of brands such as Gauloises, Gitanes and Golden Virginia.
Another big tobacco company in which the NPRF had invested is Altria, formerly the Philip Morris company.
At the end of 2013, the NPRF owned 46,277 shares in Philip Morris that were worth €1.3m at the time.
Altria controls brands such as Marlboro - the world's biggest cigarette brand - and L&M.
The NPRF has also held shares in Reynolds American, the second largest tobacco company in the United States. NPRF owned shares worth €285,000 in the company at the end of 2013. It also owned shares in Lorillard, the US owner of Newport cigarettes.
The ISIF is in the process of liquidating its investments outside Ireland and all it assets will be sold to fund Irish investment commitments as they arise.
The Exchequer generated €1.34bn in revenue from tobacco sales last year, according to the Finance Minister.